Definition

The greatest integer function is a function from the set of real numbers to itself that is defined as follows: it sends any real number to the largest integer that is less than or equal to it.

The greatest integer function of is sometimes denoted . However, the square brace notation is also used in a number of other contexts and should not always be construed as meaning the greatest integer function.

The greatest integer function is related to the fractional part function (sometimes denoted ) as follows: for any , we have: